scholarly journals Inverse spectral problem for Sturm - Liouville operator with prescribed partial trace

2020 ◽  
Vol 12 (4) ◽  
pp. 19-29
Author(s):  
Nurmukhamet Fuatovich Valeev ◽  
Yavdat Shavkatovich Ilyasov
Keyword(s):  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Partial Trace ◽  
Sturm Liouville ◽  
Inverse Spectral

scholarly journals An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
I. Dehghani Tazehkand ◽  
A. Jodayree Akbarfam
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Spectral Characteristics ◽  
Star Graph ◽  
Dirichlet Problems ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Robin Boundary

We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics,we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable.We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.

scholarly journals Solution of a model inverse spectral problem for the Sturm-Liouville operator on a graph

2016 ◽  
pp. 204-211
Author(s):  
Н.Ф. Валеев ◽  
Ю.В. Мартынова ◽  
Я.Т. Султанаев
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Dimensional Space ◽  
Geometric Graph ◽  
Finite Dimensional Space ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Model Inverse

Исследуется модельная обратная спектральная задача для оператора Штурма-Лиувилля на геометрическом графе. Суть данной задачи состоит в восстановлении $N$ параметров граничных условий по $N$ собственным значениям. Установлено, что эта задача обладает свойством монотонной зависимости собственных значений от параметров граничных условий. Поставленная задача сведена к многопараметрической обратной спектральной задаче для оператора в конечномерном пространстве. Предложен новый алгоритм численного решения рассматриваемой задачи. A model inverse spectral problem for the Sturm-Liouville operator on a geometric graph is studied. This problem consists in finding $N$ parameters of the boundary conditions using its $N$ known eigenvalues. It is shown that the problem under consideration possess the property of a monotonic dependence of its eigenvalues on the parameters of the boundary conditions. This problem is reduced to a multiparameter inverse spectral problem for the operator in a finite-dimensional space. A new algorithm for the numerical solution of this problem is proposed.

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